On the Estimation of Stress Strength Reliability Parameter of Weibull-Rayleigh Distribution
Eno E. E. Akarawak
Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria.
Matthew Iwada Ekum *
Department of Mathematical Science, Lagos State University of Science and Technology, Lagos, Nigeria.
Sheriffdeen Taiwo Oyeyemi
Department of Statistics, Federal Ministry of Health, Lagos, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The reliability of a component depends on the stress conditions of the operating environment, which are uncertainty and should be modeled as random. This article deals with the estimation of the stress-strength reliability parameter of Weibull-Rayleigh distribution. Let X and Y be two independent random variables, where X and Y follow Weibull-Rayleigh distribution. The maximum likelihood estimator and the approximate maximum likelihood estimator of the stress-strength reliability are obtained. Other properties of the Weibull-Rayleigh distributions are derived. Two real data applications are given for showing the flexibility of the Weibull-Rayleigh stress-strength reliability.
Keywords: Maximum likelihood estimation, reliability, weibull-rayleigh, stress-strength, uncertainty